April 08, 2003

More Holes Revealed in Matthew Yglesias's College Education

Today reveals more holes in future American Prospect writing fellow Matthew Yglesias's college education:

Matthew Yglesias: Square Circles: God's inability to make square circles is like God's inability to create szlactons, not like my inability to build a refrigerator. It?s not that God lacks the capacity to do it, it's just that the sentence "God could create a szlacton" doesn't attribute anything meaningful to God.

Clearly he has never read John M. Ford's story, "Scrabble with God" (in John M. Ford (1997), From the End of the Twentieth Century (Framingham, MA: NESFA Press: 0915368730)):

I don't recommend playing with God. It isn't that he cheats, exactly. But the other night we were in the middle of a game, I was about thirty points up, and He emptied out his rack. ZWEEGHB. Double word score and the fifty-point bonus.

"Zweeghb?" I said.

"Is that a challenge?"

"Well..." If you challenge God and you're wrong, you lose the points and get turned into a pillar of salt.

"Look outside," He said. So I did. Sure enough, there was a zweeghb out there, eating the rosebushes, like Thurber's unicorn.

"I thought you rested from creating stuff."

"Eighth day, I did. Now I'm fresh as a daisy. You going to pass or play?"

Any God worthy of the name had better be able to create square circles: that is, to alter the fabric of space, time, reality, thought, and truth itself in such a way that there are shapes in which every point on its edge is equidistant from the center (hence circular) and in which its edges make up four straight lines with right angles between them (hence square).

Posted by DeLong at April 8, 2003 12:59 PM | TrackBack

Comments

Speaking of God, William F. Buckley Jr. has a wonderful peice in the preface of my American Heritage English Dictionary in which he argues that neologisms are valid because he says they are, and not a moment sooner. (I'm exaggerating, but not by much.) Buckley has a point - language is rigid yet flexible, and words gain meaning when the have the sanction of the literate intellectual community.

(The contrary argument, by George Will if I recall, is that words have sanction when they have wide currency, which is to say that wannabe words become acceptable when they are known and understood by most speakers.)

The trouble with God, though I don't doubt his power to create a zweeghb on the fly, is that his authority to create neologisms is weak on account of the fact that his literary work has been through dictation (some of it of questionable quality).

I question whether or not zweeghb could be accepted as a neologism if the inventor is of dubious literary background and the word has not yet gained wide currency...

(My rule is that if it isn't in the dictionary, it's not a word. Problem solved, God loses a turn.)

Posted by: Saam Barrager on April 8, 2003 04:46 PM

I happen to like the anti-nominalism of the piece.

The narrator says that there is no such word as "zweeghb" and in response God makes a rose-eating beast. The curious thing is that the narrator instantly recognizes it as a "zweeghb." Why couldn't it have as easily been a rhinoceros, and the narrator just not know any better? For the narrator to recognize it as a "zweeghb", wouldn't he have to know the characteristics of a "zweeghb"? And if he knows that a "zweeghb" is a beast of certain shape and size, with a particular fondness for eating rose bushes, doesn't God win without having to make one? (The same goes for unicorns.)

Again, (however wrong it is) I get giddy at the idea that names of things are somehow inherently tied up in the things themselves. Perhaps God could bind names up with their objects. Like Saam, though, I can't fully trust the inherent naming abilities of one whose dictation skills are so spotty.

Posted by: Robert Tennyson on April 8, 2003 05:25 PM

But as to szlactons and God's ability to create them, I'm sure God could create anything he liked. Now, whether those things would be called "szlactons" is another story. I tend to think that's a matter of language use.
(Perhaps God could drop the name "szlacton" into the heads of speakers with a little picture of the beast, but that doesn't insure that people will use the term to refer to the beasts. Perhaps "szlaction" would come to mean little pictures dropped into the minds of mere mortals. Until we see how the term is used, we can't know what it means, and thuse whether God has, in this case, created a szlacton.
I suppose we could come up with some story of how God could create these beasts and have them be named "szlactons" at their creation, but (he says without argument) I don't know if this could be done without making language, as we use it, into something else.)
In any case, I don't think that the sentence "God could create a szlaction" can mean much more than that God can create a beast and God could have us call it a "szlacton." And rather than being a meaningless attribution to God, it is a pointless one, well within the four corners of omnipotence.
The question of God's ability to create szlactons is therefore unlike the question of his ability to make a square circle, in that the former matter is one that sits squarely within the borders of omnipotence and the latter concerns what it means to be omnipotent.

P.S. Old philosophy joke: Do you want to know what a square circle looks like?

Here's a side view: ______

Posted by: Robert Tennyson on April 8, 2003 05:55 PM

Think of a hemisphere. All its points lie at the same distance from its center. Now draw a square on that surface. There you go.
Yes, I am cheating. No, I am not God.

Posted by: Camilo on April 8, 2003 10:24 PM

"Any God worthy of the name had better be able to create square circles"

No, actually. As Aquinas pointed out at length even God is restrained by the laws of logic (though not of physics) - otherwise humans can have no understanding of either God or the world at all (Duns Scotus showed that accepting one logical contradiction anywhere allows us to prove anything we like).

Any God worthy of the name can create a square object from a circular object, but part of the ##agreed definition## of "square" ineluctably implies "not circular". The only ways out of this are to say "words only ever mean whatever ##I## want them to mean" so there is never an agreed meaning, or (a closely related post-modern view) the object is always square or circular depending on the POV of the observer.

Posted by: derrida derider on April 8, 2003 10:37 PM

"Any God worthy of the name had better be able to create square circles"

No, actually. As Aquinas pointed out at length even God is restrained by the laws of logic (though not of physics) - otherwise humans can have no understanding of either God or the world at all (Duns Scotus showed that accepting one logical contradiction anywhere allows us to prove anything we like).

Any God worthy of the name can create a square object from a circular object, but part of the ##agreed definition## of "square" ineluctably implies "not circular". The only ways out of this are to say "words only ever mean whatever ##I## want them to mean" so there is never an agreed meaning, or (a closely related post-modern view) the object is always square or circular depending on the POV of the observer.

Posted by: derrida derider on April 8, 2003 10:38 PM

What is the shape of a square circle?

Sounds more like a Zen koan a than theological proposition.

Posted by: E. Avedisian on April 9, 2003 12:17 AM

As someone who is used to this type of debate, the problem is that the common western idea of a triple-omni (omniniscient, omnipotent, omnitbenevolent) is frankly, impossible. I think that's the point.

Once that has been logically proven, it opens up a nice can of worms for theologens. Especially the whole problem of evil.

Posted by: Glenn on April 9, 2003 04:29 AM

If a circle is a set "in which every point on its edge is equidistant from the center", then the unit circle in a mathematical L1 space is a square circle. In 2 dimensional L1 space, the distance from (x,y) to the origin is |x|+|y|, so the unit circle is the set of points with |x|+|y|=1, which is a square in the (x,y)-plane.

Snarky? No, mathematicians refer, with little irony, to such things as unit circles. Of course, what we've done is to re-define "distance".

Posted by: bob cox on April 9, 2003 05:42 AM

Actually, the basic problem of demanding square circles of God lies in assuming knowledge we can't have. Since the basic question deals with distance and time, what are the implications of square circles for those of us living in distance and time?

Aquinas doesn't even have to be correct for his defense to show that the problem is a fallacy. We are not all knowing. God may be able to make square circles but it doesn't mean he should/would.

Posted by: Stan on April 9, 2003 07:03 AM

From William Blake:
To God
If you created a circle for us to go into
Go into it yourself and see how you would do."

Posted by: David on April 9, 2003 07:26 AM

Here's a link to a Stanford Encyclopedia of Philosophy page on Omnipotence:

http://plato.stanford.edu/entries/omnipotence/

Posted by: David on April 9, 2003 08:04 AM

Brad,

I'm not clear on how you understand the status of square circles.

Most philosophical discussions of them presume that they're an example of something logically impossible.

But your discussion of what might need to be changed in order to bring them about suggests, to me, that God would simply need to change the physical constraints of things. On that understanding, square circles might, in our world, be physically impossible (but not logically impossible).

Are square circles merely physically impossible, on your view?

Posted by: David on April 9, 2003 08:30 AM

An economist's view of philosophy is as entertaining as an entertainer's view of political science -- maybe even slightly better informed.

But as one would not approach Martin Sheen for serious discussion about Mugabe vs Mandela, I can't imagine asking Brad to seriously critique, oh, say, Niebuhr or Tillich. One is entitled to an opinion. One might be careful of the value one claims for it.


Posted by: Melcher on April 9, 2003 01:14 PM

This feels kind of petty in comparison to all the highbrowish remarks above, but wasn't it the 7th day that God rested? Of course, if it's His memory that it was the 8th day, far be it from me to quibble!

Posted by: David on April 9, 2003 01:34 PM

I think a bit more highly of Mr. DeLong's abilities. I'll assume he's got a reason for his opinion, until he says otherwise.

Besides, there are philosophers who make claims about economics, and economists who make claims about philosophy. It happens more often than one might think. There's even a journal, Economics and Philosophy!

http://titles.cambridge.org/journals/journal_catalogue.asp?mnemonic=eap

I suppose that Amartya Sen is a good example of the economist/philosopher. Adam Smith, too. Why not Brad DeLong?

Posted by: David on April 9, 2003 01:38 PM

Derrida Derider: "As Aquinas pointed out at length even God is restrained by the laws of logic (though not of physics) - otherwise humans can have no understanding of either God or the world at all (Duns Scotus showed that accepting one logical contradiction anywhere allows us to prove anything we like)."

Regarding Aquinas's argument that even God is constrained by the laws of logic: This used to be one of the most contested issues in philosophical theology. As equally well-entrenched as the belief that God is constrained by the limits of the logical possible is the view that any constraints at all are incompatible with God's omnipotence (according to the latter view, God has the power to legislate what is logically possible). The proponent of such a view is, as Aquinas's argument implies, forced to admit that God is inscrutable, but that didn't really bother most of the particpants in the debate (indeed, to concede that was often claimed to be a sign of piety).

Notice that Duns Scotus's argument doesn't really apply here, since one who thinks that God can legislate the laws of logic thinks of the contradictions that God makes true as ceasing to be contradictions once God decides that they're true.

There's also a widespread misapprehension lurking here, which it's worth commenting on. Duns Scotus's argument depends on some non-trivial assumptions that can easily fail to be satisfied. There are plenty of ways of representing human reasoning in formal terms which don't have the property that, once one accepts a contradiction, one can prove anything. (In fact, this property of logical systems--often called "explosion"--belongs only to a minority of the standard systems, but people get a mistaken idea of its significance because it's a major feature of the kind of logic taught in intro courses.)

Posted by: Alp Aker on April 9, 2003 01:41 PM

Thanks for clearing the air of highbrowish remarks, David!

The other thing I forgot to mention was that God would probably catch me using upside-down letter tiles as blank tiles - without even flipping them over. I wouldn't quibble, but would he smite me? I'd rather not know, which is why I only use the trick on mere mortals...

Posted by: Saam Barrager on April 9, 2003 01:50 PM

Leaving aside (bracketing) the main issue, it's curious that "square circle" is being used as the stand in for a logical contradiction. As noted by Bob Cox,from a mathematical viewpoint this depends on the choice of axioms and the definitions in the geometry,and is not at all obvious. Besides,a mathematician would be led to think of the classical problem of "squaring the circle", i.e. using only a straight edge and compass to construct a square with the same area as a given circle. This was in fact proven to be impossible in Euclidean geometry (Lindemann, 1882). However it is possible in certain non-Euclidean geometries, including possibly the one we live in, whether or not [God] created it.

Posted by: d-* on April 9, 2003 02:45 PM

"Square circle" is sort of a traditional example to use in this context, going back at least to Meinong and Brentano in the 19th century. I can't remember off-hand whether it comes up in Leibniz or Descartes or any other earlier figures who wrote on this sort of topic.

Posted by: Alp Aker on April 9, 2003 03:59 PM

"Any God worthy of the name had better be able to create square circles"

As pointed out in some comments above, Brad's statement is rooted in the (silly) idea that God is omnipotent. Hah. An omnipotent God would never have allowed some highly-strung, arrogant, self-involved twit of a philosopher to claim that God is Dead. God has a different type of existence. He is not omnipotent, and he depends on human beings, and other living things, to carry out his will in this universe.

As for physics and geometry, all one can do is be skeptical, wait, and see. It would not be surprising if FY Edgworth or Charles Dodgson, Brad's spiritual soul mates from the 19th century had claimed, "Any God worthy of the name had better be able to create divisible atomic particles." Well, there you go. Maybe there is some nth dimension where square circles exist. We'll just have to see.

Posted by: andres on April 10, 2003 09:08 AM

And on the seventh day God rested.

And sometime later, He called a Staff Meeting, with the agenda on the issue of "the sub-atomic level, and the assusrances of certain Archangels". Specifically, at about day five and half the assurances that "It's all good. It'll all compile. We'll complete the project on time", and the fact that certain humans have at the current time been making snarky statements about God, the Universe and Dice.

Ian Whitchurch

Posted by: Ian Whitchurch on April 13, 2003 05:18 AM

"The narrator says that there is no such word as "zweeghb" and in response God makes a rose-eating beast. The curious thing is that the narrator instantly recognizes it as a "zweeghb." Why couldn't it have as easily been a rhinoceros, and the narrator just not know any better?"
Adam looks at an animal and says, "I think I'll call that a tiger." Eve says, "Why?" Adam says, "Because it LOOKS like a tiger."
Anyone interested in these conundra (I guess) will enjoy The Battlefield God, which probably spurred this thread. It's a philosopher's quiz testing the inner consistency of your metaphysics. I do think this "logical impossibility" debate doesn't really address the question of the Trinity, for Christians.

Posted by: John Isbell on April 13, 2003 10:48 AM
Post a comment